Problem to Find perpendicular line from a point to a line in a coordinate system

Topic : Co ordinate System and a Line Equation

Question : Use co ordinate geometry to show the perpendicular distance between a point (x,y) and a line Ax+By+C= 0, is given by

d = (Ax+By+C) / √(A²+B²)

Solution :

Perpendicular Distance from (0,0) to the line Ax+By+C = 0 is
C
--------------
√(A²+B²)

Effecting the translation (X,Y)=>(X+x,Y+y) the equation of the line changes to :

A(X+x)+B(Y+y)+C=0
AX+BY+(Ax+By+C)=0
Perpendicular distance from the origin is :
(AX+BY+C ) / √(A²+B²) = (Ax+By+C ) / √(A²+B²)

Since the transformation here is an isometry the distance is preserved


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Question on Calculating Payment with Interest

Topic : Interest Applied on Payment.

Question : Noreen bought a house for $2,09,000. She paid 25% down and obtained 7-year mortgage at 7% per annum, amortized over 20 years. Calculate Noreen's monthly mortgage payment.

Answer :
7 year mortgage at 7% annual(assuming compounded annually)
amount = 209,000 * 0.75(since 25% is given as downpayment)= $ 156,750
Total amount with interest = 156750*(1+0.07)^7= 251,706
Monthly Amortized payments over 20 years is 251,706/240 = $1048.77

Hope the Solution is helpful for you.